Simplified implementation of the quantum Fourier transform with Ising-type Hamiltonians: Example with ion traps

TL;DR

This paper introduces a simplified quantum Fourier transform implementation tailored for Ising-type Hamiltonian systems, achieving quadratic speed-up and practical realization with ion traps using microwave control.

Contribution

It presents a novel, simplified method for quantum Fourier transform that reduces complexity and enables faster execution on Ising-type systems, especially ion traps.

Findings

Quadratic speed-up in quantum Fourier transform implementation.

Feasible realization with microwave-driven ion traps.

Reduction from O(N^2) to O(N) in implementation time.

Abstract

We propose a simplified mathematical construction of the quantum Fourier transform which is suited for systems described by Ising-type Hamiltonians. By contrast to the standard Cooley-Tuckey scheme, which prescribes sequences of CPHASE gates, our implementation is based on one-qubit gates and a free evolution process. We also show how to obtain a quadratic speed-up by applying the conditional interactions simultaneously. Thus rather than O($N^2$) our implementation time scales as O($N$). Finally, we show a realization of our method with homogeneous microwave driven ion traps in a magnetic field with gradient.